So, we can already start piecing our equation together:
oxygen content = (amount of oxygen on Hb) + (amount of dissolved oxygen)
The amount of oxygen on haemoglobin (Hb) will, in turn, depend on two self-evident variables: the Hb concentration, and the Hb's oxygen saturation. Each gram of Hb holds 1.36 ml oxygen if fully saturated, and you need to use this conversion factor too. Thus:
oxygen content = (1.36 x Hb x sats) + (amount of dissolved oxygen)
Now we can turn to the second half of the equation. The amount of oxygen dissolved in the blood depends on only one variable - the partial pressure of oxygen. In other words, the higher the oxgyen concentration of the inspired air (or other gas), the more oxygen will dissolve into the blood. As before, we need a conversion factor to help us move from partial pressure to millilitres of oxygen; this factor is known as the 'solubility coefficient' for oxygen in plasma, and is equal to 0.003.
Thus, putting everything together, we end up with:
oxygen content = (1.36 x Hb x sats) + (0.003 x PaO2)
This equation is actually quite useful - it's not all just academic. For one thing, it quantifies some of the things that one could do to improve oxygen delivery to the tissues. For instance, would it be more beneficial to give the patient an oxygen mask (which would increase the sats and the PaO2) or a blood transfusion (which would increase the Hb)? Depending what the patient's starting values are, the answer will vary, but the cool thing is that you can work it out.
Furthermore, knowledge of the oxygen content in 'mixed' venous blood has important diagnostic and therapeutic implications. That will be the topic of the next post.